Multiply the following complex numbers: $({-2+4i}) \cdot ({5-3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2+4i}) \cdot ({5-3i}) = $ $ ({-2} \cdot {5}) + ({-2} \cdot {-3}i) + ({4}i \cdot {5}) + ({4}i \cdot {-3}i) $ Then simplify the terms: $ (-10) + (6i) + (20i) + (-12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -10 + (6 + 20)i - 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -10 + (6 + 20)i - (-12) $ The result is simplified: $ (-10 + 12) + (26i) = 2+26i $